Question

The wavelength ${\lambda }_e$ of an electron and λp of a photon of same energy E are related by -

• A. ${\lambda }_e^2\propto {\lambda }_p$
• B. ${\lambda }_p\propto {\lambda }_e$
• C. ${\lambda }_p\propto \sqrt{{\lambda }_e}$
• D. ${\lambda }_p\propto \sqrt{{\lambda }_e}$

Answer 1

The correct option is A ${\lambda }_e^2\propto {\lambda }_p$

${\lambda }_e=\frac{h}{\sqrt{2mE}}or{\lambda }_e\propto \frac{1}{\sqrt{E}}or{\lambda }_e^2\propto \frac{1}{\sqrt{E}}\cdots \left(1\right)$
Wavelength of photon $\Rightarrow {\lambda }_p=\frac{hc}{E}$
or ${\lambda }_{p}directlyproportional\frac{1}{E}\cdots \left(2\right)$
From equation (1) and (2)
${\lambda }_e^2\propto {\lambda }_p$